7. Suppose that another drug is administered intravenously to an adult patient in a hospital as prescribed by a doctor. The relationship between the concentration of the drug (in mg/L) in the bloodstream and the time (in hours after administration) is modeled by the function. a) Using the function above, fill in a chart of the concentration of the drug in the bloodstream for the first 24-hour period after administration at intervals of two hours. Write the concentration accurate to two decimal places as needed. t 0 2 4 6 8 10 12 14 16 18 20 22 24 c(t) b) When will the concentration of the drug fall to a level of 0.5 mg/L? c) When must the next dose of the drug be administered to the patient in order to maintain a concentration above 1 mg/L and below 8 mg/L? Explain your reasoning. d) What is a reasonable domain for this function? Justify why (and if) you would exclude any values.

Do you use probability in your profession or real life? You most likely do. For example, the chance of rain tomorrow is 27%. We hear similar probabilities in the media all the time. Similar probabilities could be found in other professions. Complete one of the following:(i) Find an example of probability involving “A or B” that is used in your chosen profession or real life. Explain the example. Are the events A and B in your example mutually exclusive? Which Addition Rule formula for P(A or B) applies? Be sure to cite the source of the information clearly.(ii) Using a search engine, find an example of probability involving “A and B” that is used in your chosen profession or real life. Explain the example. Are the events A and B in your example independent? Which Multiplication Rule formula for P(A and B) applies? Be sure to cite the source of the information clearly.(iii) Find an example involving conditional probability that is used in your chosen profession or real life. Explain the example. Be sure to cite the source of the information clearly.

Q1 IT Department of an electronic retail company found a new computer virus, which attacks only software of smart microwave ovens made by the company. The Sales Department could call back a few batches of ovens and send them to IT guys for testing. Testing indicated version differences: Approximately 10% of the sample of last models were infected, approximately 35% of the sample of one-year-old models were infected, and approximately 50% of the sample of three-year-old models were infected. Describe the variables and indicate whether each variable is quantitative or categorical. Q2 A scientist collects data from many people to determine how the age and weight are related. How the data is collected determines whether the variables are quantitative or categorical. Describe how the information might be recorded if we regard both variables as categorical. Q3 Hybrid electric vehicles is a type of a hybrid vehicle and an electric vehicle that combines the conventional internal combustion engine propulsion system with the electric propulsion system. One study of 4250 car owners in Utah found that 14% had a hybrid car. Besides, the second study measured average gas mileage per gallon in a city and on a highway. Finally, the third study measured the maximum distance without refuel or recharging. In each of three studies, identify the variables and whether each variable is quantitative or categorical. Q4 In one study, a water sample was taken from various lakes. The data indicate that as the concentration of a large group of unicellular microorganisms in the lake water goes up, the fertility level of fish in the lake goes down. The group of unicellular microorganisms level is measured in parts per trillion (ppt) and the fertility level is recorded as the percent of eggs fertilized. Describe the variables and indicate whether each variable is quantitative or categorical. Q5 New studies suggest that experiences of parents can affect future children: Early life experiences of parents appear to cause permanent changes in sperm and eggs. In one study, some male rats were fed a high-fat diet with 43% of calories from fat with some drops of alcohol in the drinking water, while others were fed a normal healthy rat diet. Not surprising, the rats fed the high-fat food with alcohol were far more likely to develop diabetes than the rats on the normal-diet. What surprised the scientists was that the kids of these rats were also far more likely to develop diabetes than the kids of rats fed healthy diets. None of the kids and none of the mothers ate a high-fat diet with alcohol and fathers did not have any contact with kids. The high-fat diet with alcohol of the fathers appeared to cause negative effects for their kids. Describe the variables and indicate whether each variable is quantitative or categorical, and indicate the explanatory and response variables. Select the correct variables below. Q6 The dataset below contains the countries that won the FIFA World Cup more than anybody else. Brazil – 5 times (1958, 1962, 1970, 1994, 2002) – never won the home World Cup. Germany – 4 times (1954, 1974, 1990, 2014) – won the home World Cup. Italy – 4 times (1934, 1938, 1982, 2006) – won the home World Cup. How many cases are there in this dataset? What are the cases? How many variables are there in this dataset? What are the variables?